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In the present work, nonlinear free vibration analysis of composite laminated plates and shallow cylindrical/spherical/hyperboloid shell panels considering geometric nonlinearity is carried out using non-polynomial inverse trigonometric higher-order shear deformation theory with seven degrees of freedo (DOFs). The present theory assumes parabolic variation of out-of-plane stresses and satisfies traction-free boundary conditions on the top and bottom surfaces of the composite as a priori. A nonlinear finite element model is developed and applied to obtain discretized nonlinear equations. The geometric nonlinearity in sense of Green-Lagrange considering von-Kármán assumptions is incorporated in formulation. An eight noded efficient  C0  continuous isoparametric rectangular finite element is implemented in the present nonlinear analysis. The efficacy and accuracy of the present theory and finite element model is validated with the available literature results. For the analysis, various types of plates and shell panels with different material properties, lamination schemes, thickness ratios, aspect ratios, modular ratios, curvature ratios, and boundary conditions are considered. The effects of these different geometric and material properties on nonlinear frequency ratios at various amplitude ratios are examined in detail.

Nonlinear free vibration analysis of laminated composite plates and shell panels using non-polynomial higher-order shear deformation theory